Solve for $x$ and $y$ using elimination. ${-4x+y = -39}$ ${-5x-y = -51}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-9x = -90$ $\dfrac{-9x}{{-9}} = \dfrac{-90}{{-9}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-4x+y = -39}\thinspace$ to find $y$ ${-4}{(10)}{ + y = -39}$ $-40+y = -39$ $-40{+40} + y = -39{+40}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {-5x-y = -51}\thinspace$ and get the same answer for $y$ : ${-5}{(10)}{ - y = -51}$ ${y = 1}$